Why are my turnip seedlings dying?

(This was posted on my food blog Sept. 10.)

They sprouted nicely a month or so ago. Since then, wilty and dying. Why? This site explains that turnips originate from Siberia. SIBERIA! In other words, they thrive in temperatures between 40 and 75 degrees.

It's been routinely around 85 where I live, so no matter how consistently I water them or how much shade they have, the turnip seedlings are overheated. Maybe I'll wait until winter to try again. Or not. I was so looking forward to making kim chi turnip. Can't win 'em all.